The Daily Mirror is reporting that both of the Premier League clubs are keeping tabs on the 21-year-old midfielder as the January transfer window draws nearer.
It is claimed in the same report that both Manchester United and Chelsea FC are now competing with Manchester City for the signature of the talented Frenchman.
According to the same story, Manchester United and Chelsea FC both sent scouts to watch Ndombele in action when they took on Hoffenheim in the Champions League last week.
The article also credits north London side Tottenham Hotspur with an interest in the midfielder.
Ndombele has been in solid form for Lyon so far this season, notching up four assists in 11 Ligue 1 appearances for the French club to help them up to fourth place in the table.
He has also netted once in three Champions League group stage appearances so far this term, including one goal in the 3-3 draw with Hoffenheim last week.
Manchester United are likely to be linked with a number of players ahead of the January transfer window as Jose Mourinho considers adding to his squad following a stuttering start to the new season.
Chelsea FC could also be looking to sign some new names in January, despite the Blues having made an impressive start to life under new boss Maurizio Sarri following his appointment back in July.
Chelsea FC will take on Derby in the League Cup fourth round on Wednesday night at Stamford Bridge, while Manchester United travel to Bournemouth in the Premier League on Saturday lunchtime.
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news